Laboratory spectroscopy and the search for variation of the fine-structure constant

Theories unifying gravity with other interactions suggest that fundamental “constants” could (or even should) vary with time and space in an expanding Universe. The value of the fine-structure constant, $\alpha = e^2/\hbar c$ , can be probed over the history of the Universe using quasar absorption systems. On the other hand by comparing atomic clocks over some reasonably long time period (~ years) we can test whether α is currently changing with time on Earth. In this paper we discuss the some of the directions in which this research is heading and some laboratory measurements of absolute frequency and isotope shift which are much needed for these studies of α-variation. Researchers who are interested in performing these measurements should contact the authors directly.